(x+3)(x-3) Expanded

Suzhoumeite

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Jul 03, 2024

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Expanding (x+3)(x-3)

In algebra, expanding a product of binomials is a crucial skill to master. In this article, we will explore how to expand the product of (x+3) and (x-3).

What is the Product of Two Binomials?

When we multiply two binomials, we use the distributive property of multiplication over addition. This means that we need to multiply each term in the first binomial by each term in the second binomial.

Expanding (x+3)(x-3)

Let's expand the product of (x+3) and (x-3):

(x+3)(x-3) = ?

To expand this product, we need to multiply each term in the first binomial by each term in the second binomial:

• Multiply x by x: x^2
• Multiply x by -3: -3x
• Multiply 3 by x: 3x
• Multiply 3 by -3: -9

Now, let's combine like terms:

(x+3)(x-3) = x^2 - 3x + 3x - 9

Simplifying the Expression

Notice that we have two terms with the same variable x but with opposite coefficients: -3x and 3x. These terms cancel each other out:

(x+3)(x-3) = x^2 - 9

Result

The expanded form of (x+3)(x-3) is x^2 - 9.

Conclusion

Expanding the product of (x+3) and (x-3) is a simple process that involves multiplying each term in the first binomial by each term in the second binomial. By combining like terms, we arrive at the simplified expression x^2 - 9.